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Orlicz capacities and Hausdorff measures on metric spaces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-1238-6751
Department of Mathematics University of Michigan, Ann Arbor, USA.
2005 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, Vol. 251, no 1, 131-146 p.Article in journal (Refereed) Published
Abstract [en]

In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided that ∫10Θ -1(t1-sh(t))dt< ∞ where Θ -1 is the inverse of the function Θ(t)=Φ(t)/t, and s is the "upper dimension" of the metric measure space. This condition is a generalization of a well known condition in R n . For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided. © Springer-Verlag Berlin Heidelberg 2005.

Place, publisher, year, edition, pages
2005. Vol. 251, no 1, 131-146 p.
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URN: urn:nbn:se:liu:diva-30246DOI: 10.1007/s00209-005-0792-yLocal ID: 15751OAI: diva2:251068
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2016-05-04

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